It’s difficult to generalize because we’re talking about such a wide geographic and historic era, but...in Islamic lands, generally Jews were not treated differently from other religious minorities simply because they were Jews. (In some cases they were treated better because as a non-proselytizing population they were seen as non-threatening.) Jews fared well under Muslim rulers that tended to be tolerant and supportive of minority populations, and they fared poorly under Muslim rulers that didn’t.

Under the Umayyads Al-Andalus, for example, is considered one of the Golden Ages of Jewish history—there were Christians and Jews at court, and the Umayyad caliph’s chief surgeon was a Jew; but the Umayyads were replaced by the Almohads who believed that religious minorities, as subjugated peoples, needed to be treated as such and laid down much stricter laws (this is one of the reasons why Maimonides moved to Cairo, for example).

Overall, however, the decline in specific Muslim-Jewish relations (as differentiated from Islam’s relationship to other faiths) is relatively new and can be linked to the 20th century Arab-Israeli conflict.

If there is a specific time and place that you’re interested in, I can try to point you in the direction of further reading.

Well, it depends what you're looking for, in some cases. Some places now with a predominantly Muslim population were not always historically, some places had Muslim rulers with large non-Muslim populations, and some places had large Muslim populations with non-Muslim rulers. For the purposes of the answer, I will try to account for the treatment of Jews and Samaritans within Islamic realms, during the rise of Islam, and in highly Islamic areas even under Christian rule.

Pre-1500

So, the first negative interaction Islam has with Jews occurs in the ancient Arabian city of Yathrib, modern Medina. The historicity of this event has been called into question, particularly the question of scale, but as it represents an early Islamic narrative about their prophet, it could be taken to consider attitudes even if not necessarily historical reality. According to early Islamic sources, this city was a Jewish trade colony originally, ruled by 3 Jewish tribes known in Arabic as the Banu Qaynuqa, the Banu Qurayza, and the Banu Nadir. They also report that the Qurayza had been administrative officials under the Sassanid governance of the region in the past. Muhammad came into this area and tried to establish a treaty to end intertribal conflict, essentially establishing a base of power, that was ultimately challenged by the locals. The Jewish tribes were, each in turn, massacred and expelled, and in each case with accusations of hostility, deception, and/or betrayal, which can be reflected in the modern antisemitic canard of the scheming Jew.

While I must say again that the historicity has been called into question, this would at the very least be reflective of early attitudes towards Jews, depicting them as murderous and impious schemers, enemies of the prophet. Several tribes who had reportedly converted to Judaism as some point were not treated as harshly, and ultimately converted to Islam. During Muhammad's lifetime, the region of Yemen had a large Jewish population, largely Himyarite converts, and the area became a small hotbed of religious tensions for a while as the locals began to shift gradually to Islam.

It was not long after Muhammad that some of the first persecutions came into place. Caliph Umar, the second Caliph, besieged Jerusalem in 637 CE. During this time, amidst the chaos of changing government, the contemporary Armenian bishop Sebeos wrote that the Jews made another attempt at constructing a Third Temple - this being the 4th or 5th attempt as Roman authorities flip-flopped and local Christians may have sabotaged the efforts - and Umar signed a treaty with the Christian Greco-Syrian population of the city that would expel the Jews from Jerusalem and destroy their efforts at building a Temple.

Jews, like other Peoples of the Book, lived as dhimmi in the medieval Islamic world. While this was nominally a protected status, it bore with it economic disincentives. The jizya tax was an alternative tax for non-Muslims, meant to replace the Islamic forms of tithe called zakat and khums. The jizya, though originally intending to be fair and accounting for the troubles of those involved, was frequently used as a political weapon. Taxation rates for Jews in cities such as Jerusalem, when Umar's decrees were not fully upheld, tended to be high enough to prevent permanent settlement in the city in large numbers. As Islam features quite a lot of imagery and symbols of submission of one form or another, frequently to God for the Muslims themselves, jizya was also form of submission for the dhimmis, a tribute for the protection, governance, and autonomy that Muslim rulers might grant them. Some Muslim scholars argue it serves the explicit purpose of an economic incentive to convert, and that allowing dhimmi to live among Muslims is only to serve such a purpose, rather than for their benefit. Thus, through the breaking of its original design in alms and charity, the weaponization of jizya is another form of antisemitism that was perpetuated throughout the Muslim world historically. In effect, Jews lived as Second-Class citizens.

Now, as with Christian realms, not all Muslim realms were intolerant, and some were quite accepting. It is heavily dependent on time and place. Let's take Spain as an example, for the Andalusian rule is sometimes considered a Jewish Golden Age. It was this setting that birthed the likes of Maimonides and Samuel haNagid. Both of these men, however, also faced intolerance as well as acceptance. Samuel, who was born in the last decade of the 10th century, started his adulthood out in Cordoba. He was forced to flee when the city was besieged and sacked by internal elements, and he established himself instead in the Taifa of Grenada. Samuel ascended to Viziership, quite controversial since he was still a dhimmi, but the government itself was tolerant of this even if it might've been taboo. Samuel's story is a great success, but we mustn't get lost in the image. You did ask for antisemitism, after all.

Samuel's prominence earned the scorn of many Muslim citizens. While he governed successfully as a vizier and general, his son, who followed in his footsteps, was lynched at the end of the year 1066. The following day, around the time of New Years Eve or so, the city's Jewish population as massacred now that the tolerant emir and his Jewish vizier were gone. It would only be a generation later that the slowly recovering community was massacred again by the invading Almoravids. Things only get worse under the Almohads, where dhimmi status was essentially revoked and Jews were put into a "convert or die" situation. Many were slaughtered, and those who converted were forced to wear identifying clothing so as not to be mistaken for 'pure' and 'sincere' Muslims. This is similar to other countries, where Jews were forced to wear patches or other identifying marks, but is more extreme in that other countries would lift this burden upon conversion to Islam. It was the Almohads whose expulsions and persecutions drove Maimonides to Egypt, where he found a much greater level of tolerance.

Indeed, leaving Spain and the Maghreb, we turn now to Egypt - one of the most ancient centers of Judaism apart from Israel itself. Egypt had, by the 12th century, had a continuous community for over a millennium and a half. Alexandria was, by that point and for a long time before, the center of both Coptic Christianity and Egyptian Jewry. It was a hotbed of dhimmis, but in Egypt, dhimmis were a majority for quite some time, and the Muslim lords acknowledged and accepted this. The Cairo Geniza, a rich source of medieval Jewish history and tradition, was composed in Muslim Egypt, and the rule was generally favorable to them. This changed, for a bit, with the sultan al-Hakim. Hakim took liberties in crushing the dhimmi back down to their place, in his view, starting with banning certain holidays and also the production and consumption of wine even for those whose religions did not forbid it. He ordered as well that Jews and Christians had to wear black belts and turbans, with Jews also wearing a wooden calf or a bell, and Christians a metal cross. Both served to ease segregation and burden the wearer with heavy neckwear. Non-Muslim women had to wear unmatching shoes as well. He began to destroy houses of worship and force conversions, only starting to ease up in the latter days of his reign. Other than this peculiar man, though, Jews in Egypt were generally tolerated to a fair degree until Mamluke rule.

Under the Mamlukes, persecution against Jews started to take on more familiar characteristics and scale. Jews were forced to wear yellow turbans and wear signs, were banned from public bathhouses (and, thus, public hygiene services), and the ban of holding offices that is often drawn to Caliph Umar was reinforced. All this to say nothing of all the stuff going on in the Levant which, although ruled traditionally by Egypt, often had its own business going on.

So, the Levant. There is some evidence to suggest that, at the time of Muslim conquest, it might've had a Jewish-Samaritan majority yet - namely, the rise of revolt against Byzantine authority while the Romans fought the Persians. However, for most of the Middle Ages, the Levant had an Aramaic-speaking Greco-Syrian Christian majority.

I've previously written up a couple answers to very similar questions here:

https://www.reddit.com/r/AskHistorians/comments/287ll0/i_have_heard_that_during_the_middle_ages_it_was/ci8dai0/

https://www.reddit.com/r/history/comments/2beg97/what_are_your_personal_historical_pet/cj617jx/